On the Embedded Primary Components of Ideals (IV)
The results in this paper expand the fundamental decomposition theory of ideals pioneered by Emmy Noether. Specifically, let I be an ideal in a local ring (R, M) that has M as an embedded prime divisor, and for a prime divisor P of I let be the set of irreducible components q of I that are P-primary (so there exists a decomposition of I as an irredundant finite intersection of irreducible ideals that has q as a factor). Then the main results show is maximal in the set of Al-primary components of is an irredundant irreducible decomposition of I such that is Af-primary if and only if i = 1,., k < n, then is an irredundant irreducible decomposition of a MEC of I, and, conversely, if Q is a MEC of I and if is an irredundant irreducible decomposition of such that q1,., qkare the A/-primary ideals in then m = k and is an irredundant irreducible decomposition.
Heinzer, William, L. J. Ratliff, and Kishor Shah. "On the embedded primary components of ideals. IV." Transactions of the American Mathematical Society 347, no. 2 (1995): 701-708.
Transactions of the American Mathematical Society